Lipschitz representations of subsets of the cube
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Description
We show that for any class of uniformly bounded functions H with a reasonable combinatorial dimension, the vast majority of small subsets of the n-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space.
Collections | ANU Research Publications |
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Date published: | 2007-11-14 |
Type: | Journal article |
URI: | http://hdl.handle.net/1885/100414 |
Source: | Proceedings of the American Mathematical Society |
DOI: | 10.1090/S0002-9939-06-08620-5 |
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